[代码资源] 用对分法解超越方程

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发表于 2016-10-12 23:05 |只看该作者 |倒序浏览

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范例：用对分法求方程在(0,1)内的根，要求误差不超过0.1；
求解程序如下：

clear;clc;close' X5 @) @, E5 e& l$ A
% n=input('请输入迭代次数：');
+ }9 ~! |& E+ \- N) N
% qujian=input('请输入初始区间：');! `) Y/ {/ H7 o$ [
n=100;) s1 Y- P( z5 f% [
wucha=0.005;
6 b6 R1 J! K\" Z- m
qujian=[0 1];% O, {1 M3 c# ^* O+ D+ `
a(1)=qujian(1);
: S0 Q\" Y; |, i
b(1)=qujian(2);
# m& K$ E& Y6 A% q1 {4 U6 U
a0=a(1);, S! ~- M# `4 p$ D& Z1 C, i
b0=b(1);\" R. y1 H! _7 V. H$ G
x=qujian;. [/ v) t3 P) @$ o5 i\" |* |
y=exp(x)+10*x-2;
y1=y(1); %小于0
+ b# e\" ?: E+ x& }& Z' I3 y
y2=y(2); %大于0
: m5 a. I6 n# M; q
for i=1:n %总迭代次数+ P/ x/ W; U; F% q; }. u8 m\" z
c(i)=(a+b)/2;* k$ z$ w. n1 p ]$ X
f(i)=exp(c(i))+10*(c(i))-2;
2 b2 X1 u3 s. R r$ k
kesai_k(i)=(b-a)/2;
8 V h( d i( @/ E/ O
if f(i)>0
% C( }4 H, o( P1 ?8 Z8 Y) a/ r
b=c(i);7 M5 U\" n; Q4 `- }0 l. L! S/ H% H
b1(i)=c(i);* {+ l3 t0 Q0 x# y
a1(i)=a;) }, H5 h! `# f
elseif f(i)<06 A- d9 e1 P& H/ }2 o: w
a=c(i);
# C3 S/ i9 `$ U% x, p8 Z9 O
a1(i)=c(i);
+ Q: d: _1 Q2 v- Q6 Q
b1(i)=b;
, K0 R) _) {# g\" [
elseif f(i)==0||kesai_k(i)<=wucha
$ S( O/ r( v4 F, u( O
disp('精确值解为：');
# F# k\" \. U( B( g X3 Q
disp(c(i));0 T6 f- E& p+ s# m2 C( \: q
break;- y, w, J4 ^/ V
end. y; n8 \, j* Y P3 U* j
end
& _\" P- }4 @4 V% ]- I* Y
disp('迭代次数：');
) g2 I9 f4 ?' P\" |9 r
fprintf('%d次\n\n',n);2 ~7 M) [2 {8 h
fprintf('要求误差%f\n\n',wucha);0 s! h5 l* m# k4 S/ B$ q' ^( {
disp('输出矩阵为：');
+ x! p% n' Z) |9 E6 i
A=[a0 a1]';8 T7 R+ @, W) e9 t1 j4 A
B=[b0 b1]';; o5 U4 {% j( Q% A) {
format long
2 N% ]$ a( }+ N2 ~
data_out=[A B c' f' kesai_k']
7 z$ x1 j4 f4 {( ~
xlswrite('二分法处理数据.xls',data_out);

复制代码

结果输出情况：

精确值解为：
' L5 l( r) T6 U/ U\" b( U6 T
0.0905
1 U) }, X' _7 k5 b1 }+ Z* a S4 j2 k
$ I; l- Q) k4 h; M3 z
迭代次数：% W- |\" Y# l- d4 ]6 {( t4 E) H
100次
' p; r5 X\" _8 m8 _
9 w% H! v* h6 J- c8 b
要求误差0.005000# {4 v( ]3 O H4 B4 D2 s; v, W8 {0 |' Z
$ d S; [\" c5 M1 Y+ J
输出矩阵为：6 N0 s3 k2 @\" l( F8 V+ c* m& }2 [\" X\" |
' m5 A- s\" y\" Y
data_out =
# B0 ? @3 G6 [* J* t1 W
2 C) o: U3 Z( l6 O
0 1.000000000000000 0.500000000000000 4.648721270700128 0.5000000000000000 e- G3 J! x o
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000
/ z; J6 U) V5 M\" O2 [% J\" Z) |7 H
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000
6 d. F9 ]5 x\" P) ]
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.0625000000000009 [+ T' b( T/ j! C5 y% @
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.0312500000000005 K( O\" k! v, q1 M, X1 S
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.0156250000000008 R% W- h3 {; o% |: v# u$ S
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000
1 W8 l2 ~2 x& q) R9 L
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000. V5 u, W7 E3 G' Y) }4 W5 o
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.0019531250000006 B* ^, d\" U7 i- Q4 f5 v
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000
1 ]$ r\" o' @; F- d' d
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000
! C& l& H3 N# O1 i, N' B
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000/ G1 [\" |2 A: V! d& u9 X* R
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500+ q5 C1 _' l. ~9 n8 F' i {
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250+ B% h& I9 R; |& [1 z
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.0000305175781254 K) q( g [1 g1 w$ Q* g. J( E/ i# \
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063* R& K8 J* n# I$ p+ ]4 r0 z f
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.0000076293945314 Q1 E% O\" c5 e\" }: J: r+ z
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266( e\" `+ L& |. F* k0 C
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633 p; t\" P$ u, B5 d# d6 v! ^
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316
: p. H* V6 F4 B
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158
5 C; A1 Q\" }! D- S+ s' T$ y+ k
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579
% O! B2 b- ^* D\" H0 `% S/ q3 M
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290
' O8 Q; c7 E0 |
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645) y6 Y+ ^0 |% e/ b
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322
+ e\" I: `$ l& {8 y- U$ ^$ j
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161( N) r# k- q; }) P! H1 @
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581
9 E; _& e* [7 W7 m
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290
* f% \) F6 g9 L( Z
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645
% G\" m1 H( Q- B1 j; ~8 m8 }
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323
0 o1 x u* X) ?; { W8 ^
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661
2 C# i9 ?: G7 K( W% w z) }
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.000000000232831, @' A9 J8 M8 A: c3 Y
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.0000000001164158 b& x# E% Y% s' y) g9 c
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208# |3 x9 M& M j$ ]
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104
* F' C4 r. B2 {
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552
. D5 x+ c! z# n# y9 X
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276) O. b- Q4 ~8 n' K0 g3 F
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638
6 q3 {# n$ X8 U+ v- h' W
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.0000000000018193 |+ m; q! z5 O1 i9 S4 c R, |
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909
0 T$ G7 e' j% D& H: H
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455+ E( H: p( R6 H% V
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227 j% T) l8 u; e. E; G9 P, I
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114* B! j' L, t2 D\" ]% t
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057
( H2 X4 O* b* e& F- Q) N
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028
( J( [- O3 \* B/ V
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014! B& q7 ?7 t) g; u
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007 @0 T. B: i/ U
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004
; I5 b8 E+ b: n+ \7 g
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002
( i) Z$ p8 V' X
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001
: b- O7 m\" N& v+ _6 s! ]
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000